Respuesta :
Answer:
Number of participants remaining after n rounds of play, p(n) = 2¹⁶⁻ⁿ
Step-by-step explanation:
This is an example of geometric progression,
Let p(n) represents the number of participants remaining after n rounds of play.
First term = 65,536
[tex]\texttt{Common ratio = }\frac{1}{2}[/tex]
We have
[tex]p(n)=a\times r^{n}\\\\p(n)=65536\times \left (\frac{1}{2} \right )^{n}=2^{16}\times \left (\frac{1}{2} \right )^{n}\\\\p(n)=2^{16-n}[/tex]
Number of participants remaining after n rounds of play, p(n) = 2¹⁶⁻ⁿ
By using formula of general term of GP we got that formula to model the number of participants remaining is [tex]P(n)= 2^{16-n}\\[/tex]
What is a sequence ?
A sequence is collection of numbers with a particular pattern.
Given that A huge Ping-Pong tournament is held in Beijing with 65,536 participants at the start of the tournament. Each round of the tournament eliminates half the participants.
Hence number of participants remaining after 1st round = 65536/2=32768
Number of participants remaining after 2nd round=32768/2=16384
Hence this sequence is a GP with common ratio 1/2 and first term 32768
We know that general term of a GP can be written as
[tex]P(n)= ar^{n-1}[/tex]
Here a= 32768
r=1/2
So formula to model the number of participants remaining can be written as
[tex]P(n)=32768\times(\frac{1}{2})^{n-1}[/tex]
[tex]P(n)= 2^{15}\times(\frac{1}{2})^{n-1}\\\\P(n)=2^{15}\times2^{1-n}\\\\P(n)= 2^{16-n}\\[/tex]
By using formula of general term of GP we got that formula to model the number of participants remaining is [tex]P(n)= 2^{16-n}\\[/tex]
To learn more about sequence visit :
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